Corso di laurea in Chimica e Tecnologie Chimiche

Provide formal and conceptual tools for understanding the chemical complexity; opening to a quantum-mechanical approach to chemistry.

Students must acquire the competences listed below, detailed following the Dublin descriptors:

The course provides an introduction to the atomic and molecular quantum theories. It covers the fundamentals of quantum mechanics with its postulates and theorems. We illustrate the reference models (the free particle, the molecule that rotates or vibrates, the hydrogen atom) and techniques (variational method and perturbation theory, group theory). The electronic structure of the molecules (with references to the atomic states and the condensed state) and the information that can be drawn from the rotational and vibrational spectroscopy are the primary focus of the course. The full program is as follows:

1. Notes on mathematics and linear algebra.
2. Group Theory. Symmetry elements and operations, order of a group. Classes. Multiplication table. Bases and representations. Character tables and their vector interpretation. Reducible Representations (RR) and their decomposition. Symmetry of the translation, rotation and vibration motions of molecules. IR and Raman vibrational activity.
3. Introduction to quantum mechanics (QM). The inadequacy of classical mechanics at the atomic scale: black body; photoelectric effect; electron diffraction and wave/particle dualism; atomic emission spectra. The spectrum of the hydrogen atom. Heisenberg's uncertainty principle.
4. The quantum wave equation and the Schröedinger equation (EdS). EdS as an eigenvalue problem. Postulates of quantum mechanics and their meaning. Wavefunction and probability. Wavefunction requirements.
5. QM applied to simple systems: (a) particle in the box (one- and three-dimensional); (b) the harmonic oscillator (and the vibrations of the molecules); (c) the rigid rotator.
6. Approximate methods and perturbation theory. Examples for anharmonic oscillator and H and He atoms. The variational method (linear and non-linear): connections with linear algebra and the use of the calculator. The LCAO method and the H2 molecule.
7. Atomic structure. The hydrogen atom (short discussion): EdS; separation of variables; explicit solution of the part in φ. Eigenvalues ​​and eigenvectors, degeneracy and graphical representation. Nodes and nodal surfaces. Atomic orbitals (AO). Angular momentum and connection with the rigid rotator. Meaning of the quantum numbers l and m. The Spin. Level scheme and spectroscopy of the H atom. Representation of wave functions. Polyelectronic atoms: aufbau and construction of the periodic system. Configurations, states and termination symbols. The antisymmetry principle and the Slater determinant.
8. The H2+ molecule. Setting the EdS and Born-Oppenheimer approximation. The LCAO method and the molecular orbitals of H2+.
9. Simple diatomic homo- (H2, Li2, B2, C2, N2, O2, F2) and hetero-nuclear (CO, HF and NaCl) molecules. Hybridization: methane, ethylene and acetylene. Hückel's method. Conjugated systems and electronic delocalization. Aromatic molecules: benzene.
10. The matter-radiation interaction. Notes on the theory of time-dependent perturbations. Field-dipole interaction and magnetic spectroscopies. Absorption and emission probabilities and Einstein coefficients. Notes on LASERS. The experimental study of matter-radiation interaction. The electromagnetic spectrum and the main spectroscopic techniques.
11. Rotational spectra of diatomic molecules. Number, arrangement and intensity of the bands. Effect of T (Boltzman distribution).
12. Vibrational spectra: insights based on the models developed in the first part. Introduction to Raman spectroscopy.
13. Electronic spectra. Franck-Condon principle and vibronic structure. Chromophores. Fluorescence and phosphorescence 

Frontal lectures with the use of the blackboard and projection of support slides. During the lessons, simple exercises similar to those proposed in the exam will be carried out, with the aim of training students to use theoretical knowledge to solve questions of a chemical-physical nature.

The exam test aims at verifying the basic knowledge acquired by the student on the principles and methods of quantum mechanics and the capabilities (including critical reasoning) in applying it to the description of the structure (electronic configuration, bonds, geometry, etc.) and of the chemical-physical properties (stability, electrical properties, chemical properties, spectroscopy, etc.) of atoms and molecules.
The exam consists of written test structured in a series of open questions and numerical exercises on the teaching topics. To each question and/or exercise a partial score is assigned (in fractions of 30) that takes into account the specific difficulty, in terms of both the required knowledge and the time needed for response. The final vote is obtained by the sum of the partial scores, up to a maximum of 30/30 and Lode. The duration of the exam is typically set at 2 hours and a half.

If the final grade is close to passing, a brief oral exam on the most critical topics will be required Professors in cases where the written exam is sufficient but shows significant gaps in some parts of the program. Finally, any student wishing to improve their written exam grade may request the oral supplement. If the oral exam is not sufficient, the written exam must also be repeated.

Textbooks:

- P. Atkins & J. De Paula, Physical Chemistry, Oxford

Other textbooks:
- G. K. Vemulapalli, Physical Chemistry, Edises.
- D. A. McQuarrie; J. D. Simon, Physical Chemistry. A molecular approach, USB.
(Note: This text is not publlished anymore. Students can find copies of it in the chemistry library.

- Slides presented in class.

Attendance: not required, but strongly recommended.

Students with specific learning disabilities (SLD) or disabilities are requested to review the support (https://www.unito.it/servizi/lo-studio/studenti-e-studentesse-con-disabilita) and reception (https://www.unito.it/accoglienza-studenti-con-disabilita-e-dsa) procedures of the University, and in particular the procedures necessary for support during exams (https://www.unito.it/servizi/lo-studio/studenti-e-studentesse-con-disturbi-specifici-di-apprendimento-dsa/supporto)."